A certain inversion problem for the ray transform with incomplete data.
A conjecture of Gy. Petruska.
A direct method for boundary integral equations on a contour with a peak.
A factorization method for an inverse Neumann problem for harmonic vector fields.
A Liapunov functional for a linear integral equation.
A perturbed integral geometry problem in a three-dimensional space.
An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data
We propose an adaptive finite element method for the solution of a linear Fredholm integral equation of the first kind. We derive a posteriori error estimates in the functional to be minimized and in the regularized solution to this functional, and formulate corresponding adaptive algorithms. To do this we specify nonlinear results obtained earlier for the case of a linear bounded operator. Numerical experiments justify the efficiency of our a posteriori estimates applied both to the computationally...
An Adaptive Numerical Method for Solving Linear Fredholm Integral Equations of the First Kind.
An operational Haar wavelet method for solving fractional Volterra integral equations
A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the validity and applicability of the developed method.
Boundary integral equations of plane elasticity in domains with peaks.
Boundary value problems and controllability of linear systems with right invertible operators [Book]
Continuous dependence of inverse fundamental matrices of generalized linear ordinary differential equations on a parameter
The problem of continuous dependence for inverses of fundamental matrices in the case when uniform convergence is violated is presented here.
Eine Verschärfung der Poincaré-Ungleichung
Entropy of -valued operators and diverse applications.
Exponential convergence of hp quadrature for integral operators with Gevrey kernels
Galerkin discretizations of integral equations in require the evaluation of integrals where S(1),S(2) are d-simplices and g has a singularity at x = y. We assume that g is Gevrey smooth for xy and satisfies bounds for the derivatives which allow algebraic singularities at x = y. This holds for kernel functions commonly occurring in integral equations. We construct a family of quadrature rules using N function evaluations of g which achieves exponential convergence |I – | ≤C exp(–rNγ) with...
Exponential convergence of hp quadrature for integral operators with Gevrey kernels
Galerkin discretizations of integral equations in require the evaluation of integrals where S(1),S(2) are d-simplices and g has a singularity at x = y. We assume that g is Gevrey smooth for xy and satisfies bounds for the derivatives which allow algebraic singularities at x = y. This holds for kernel functions commonly occurring in integral equations. We construct a family of quadrature rules using N function evaluations of g which achieves exponential convergence |I – | ≤C exp(–rNγ) with...
Fractional integration on Hardy spaces
General linear boundary value problem for the second-order integro-differential loaded equation with boundary conditions containing both nonlocal and global terms.
Integral equations of the third kind
Integral equations, Volterra equations, and the remarkable resolvent: contractions.